\(W\) solutions of the CW equation for flow friction. (English) Zbl 1291.76178
Summary: The empirical Colebrook-White (CW) equation belongs to the group of transcendental functions. The CW function is used for the determination of hydraulic resistances associated with fluid flow through pipes, flow of rivers, etc. Since the CW equation is implicit in fluid flow friction factor, it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas developed by many authors. Alternate mathematical equivalents to the original expression of the CW equation, but now in the explicit form developed using the Lambert \(W\)-function, are shown (with related solutions). The \(W\)-function is also transcendental, but it is used more general compared with the CW function. Hence, the solution to the \(W\)-function developed by mathematicians can be used effectively for the CW function which is of interest only for hydraulics.
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 33C90 | Applications of hypergeometric functions |
Keywords:
Colebrook-White equation; Lambert \(W\)-function; turbulent flow friction; hydraulic resistance; analytical approximationsSoftware:
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